846 



Fishery Bulletin 98(4) 



Table 2 



Estimated parameter values and 95% confidence intervals (in parentheses) for each relationship between the spawning area (A,,: 

 103 kni2) and the spawning biomass (B ilO^metric ton) of Japanese pilchard along the Pacific Coast of Japan from 1978 to 1995. 



Relationship 



I 

 II 



A.,=ii,B 



A,=u,B+U2 



III A.,=u,B''-^ 



IV A,=i/,e.vp(((,>B) 



V A, = Ah'{u,/{u,+u.,B)} 



0.03196 

 (0.031853-0.032075) 



0.01141 



10.011389-0.011438) 



12.304 



(12.2926-12.3154) 



116.780 



(116.5000-116.9103) 



0.1176 

 (0.11737-0.117766) 



A (lO^/km-) 



AIC 



102.382 



(102.2073-102.5608) 



0.3156 



(0.31546-0.31567) 



0.00005689 



(0.00056782-0.000057001) 



0.0004710 

 (0.00046983-0.00047289) 



640 



48.7 

 4.7 

 0.9* 

 7.5 

 3.3 



other relationships, except for V. The optimal relationship 

 between A, and B was Aj=2.518 B"^'"" (Table 1, Fig. 6), 

 although the difference in AIC between relationship III 

 and V was small. Relationship III was statistically sig- 

 nificant (7-^=0.833, n = 18, P<0.001). A., expanded steadily 

 from 144,000 km^ in 1978 to 327,000 km- in 1988 (Fig. 

 5). The area decreased to 208,000 km- in 1989, peaked 

 at 349,000 km^ in 1990, and then shrank to 82,000 km^ 

 in 1995. The optimal relationship between A.-, and B was 

 A,,= 12.304B"^^''^'' (Table 2, Fig. 6) and was statistically sig- 

 nrficant(r-=0.737, ;! = 18,P<0.001). 



Discussion 



The spatial distribution of pilchard eggs may increase 

 over time through transportation by wind-driven currents 

 or the Kuroshio frontal eddy current (Kasai et al., 1992). 

 Because the data for calculating Ao included the presence 

 of eggs at stages long after spawning had occurred. A, 

 was an overestimate of the spawning area. Therefore, A, 

 may be a better indicator of the spawning area than A^. 

 The relationship between Aj and A^ was A, = 0.8501 

 Aj -18.468, and was statistically significant (7-=0.900, 

 n=18, P<0.001). However, the calculation of A, was more 

 expensive and time consuming because egg developmental 

 stages need to be distinguished. Selection of the indicator 

 will depend on our demand for the precision of biomass 

 estimate. 



One cause of the nonlinear relationship between the 

 spawning area and spawning biomass seemed to be that 

 pilchard egg aggregations are distributed over space in 

 a patchy manner, in relation of course to the schooling 

 behavior of the adults. Judging from the small difference 

 in AIC between relationship III and V (Table 1) and the 

 similar shapes of III and V (Fig.7), we believed that the 

 model which assumes a patchy egg distribution seemed 

 reasonable. 



An estimate of pilchard spawning biomass can be 

 obtained by using the inverted relationship of III (6= 



400 



g 300 



£ 200 



c 

 c 

 S 



g 100 



• Al 

 o A2 



5,000 10,000 15,000 20,000 



Spawning biomass (x lo' ton) 



Figure 6 



Relationship between the spawning area (A, or 

 A,,) and spawning biomass of Japanese pilchard. 

 Closed circles = the spawning area (A,), open 

 circles = the spawning area (A^). The solid line 

 indicates the optimal relationship between A, 

 and the spawning biomass (B ) (A,=0.2518B" ^«'"). 

 The dotted line indicates the optimal relation- 

 ship between A,, and the spawning biomass 

 (A,,= 12.304B""'^'''), 



0.13.5Aj2"'SM. This estimate of spawning biomass might 

 be useful as an abundance index for tuning VPA, such 

 as the adaptive framework described by Gavaris (1988). 

 Frequently, fisheries managers must estimate the bio- 

 mass of pelagic stocks. Several techniques of abundance 

 estimation may be successfully applied to the pilchard, 

 including the egg production method, acoustic surveys, 

 systematic aerial surveys, or combinations of these (Wata- 

 nabe, 1983: Hara, 1983: Hara, 1986). Selection or devel- 



